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kompoz [17]
3 years ago
15

Given an arithmetic sequence with a3=5 and a5=19, find the 24th term.

Mathematics
1 answer:
krok68 [10]3 years ago
5 0

The 24th term is 152

Step-by-step explanation:

The formula of the nth term of an arithmetic sequence is:

a_n=a+(n-1)d , where

  • a is the first term
  • d is the common difference between consecutive terms

The third term means n = 3

∵ a_3=a+(3-1)d

∴ a_3=a+2d

∵ a_3 = 5

- Equate the right hand sides of the third term

∴ a + 2d = 5 ⇒ (1)

The fifth term means n = 5

∵ a_5=a+(5-1)d

∴ a_5=a+4d

∵ a_5 = 19

- Equate the right hand sides of the fifth term

∴ a + 4d = 19 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate a

∴ 2d = 14

- Divide both sides by 2

∴ d = 7

- Substitute the value of d in equation (1) to find a

∵ a + 2(7) = 5

∴ a + 14 = 5

- Subtract 14 from both sides

∴ a = -9

The twenty fourth term means n = 24

∵ a = -9 and d = 7

- Substitute the values of a and d in the formula of the nth term

∴ a_24=-9+(24-1)(7)

∴ a_24=-9+(23)(7)

∴ a_24=-9+161

∴ a_24=152

The 24th term is 152

Learn more:

You can learn more about the arithmetic sequence in brainly.com/question/7221312

#LearnwithBrainly

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3 years ago
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Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41 % of the viewing audience in the a
ZanzabumX [31]

Answer:

1) Null hypothesis:p\geq 0.41  

Alternative hypothesis:p < 0.41

2) \hat p=0.36 estimated proportion of people indicated that they watch the late evening news on this local CBS station

3) z_{crit}=-2.33

And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

4) z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{1000}}}=-1.017  

5) z_{crit}=-1.28

And we can use the following excel code to find it: "=NORM.INV(0.1,0,1)"

6) We see that |t_{calculated}| so then we have enough evidence to FAIL to reject the null hypothesis at 1% of significance.

7) Null hypothesis:p\geq 0.41  

Step-by-step explanation:

Data given and notation  

n=100 represent the random sample taken

X represent the people indicated that they watch the late evening news on this local CBS station

\hat p=0.36 estimated proportion of people indicated that they watch the late evening news on this local CBS station

p_o=0.41 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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Alternative hypothesis:p < 0.41

Part 2  

\hat p=0.36 estimated proportion of people indicated that they watch the late evening news on this local CBS station

Part 3

Since we have a left tailed test we need to see in the normal standard distribution a value that accumulates 0.01 of the area on the left and on this case this value is :

z_{crit}=-2.33

And we can use the following excel code to find it: "=NORM.INV(0.01,0,1)"

Part 4

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.36 -0.41}{\sqrt{\frac{0.41(1-0.41)}{1000}}}=-1.017  

Part 5

Since we have a left tailed test we need to see in the normal standard distribution a value that accumulates 0.1 of the area on the left and on this case this value is :

z_{crit}=-1.28

And we can use the following excel code to find it: "=NORM.INV(0.1,0,1)"

Part 6

We see that |t_{calculated}| so then we have enough evidence to FAIL to reject the null hypothesis at 1% of significance.

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Help!! Please im having trouble
bekas [8.4K]

Answer:

1.  5/6 ≥ 2/3

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4. I can't see it's out of the pic

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6. 2/5 ≥ 2/6

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8. I can't see it's out of the pic.

9. 8/10 ≥ 3/4

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12. Can't see :(

13. 3/8 ≤ 7/8

14. 2/4 = 4/8

15. 6/8 ≥ 8/12

16. Can't see

Step-by-step explanation: All you have to do is divide the numerator by the denominator to make it into a decimal. For instance....

5/6 = approximately 0.83

I hope this helps you! It took forever....



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Answer:

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since G is disturbing a from standing alone, we divide both sides by G

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